Plasma and Fusion Research: Regular Articles

Volume 10, 3402066 (2015)

Comparison between Non-Inductive Plasma Current Start-Up
Using ECRH with and without Fundamental Resonanceon QUEST∗)Hiroki MIURA, Kazuaki HANADA1) , Hideki ZUSHI1) , Kazuo NAKAMURA1) ,Akihide FUJISAWA1) , Hiroshi IDEI1) , Yoshihiko NAGASHIMA1) , Makoto HASEGAWA1) ,Hisatoshi NAKASHIMA1) , Shoji KAWASAKI1) , Aki HIGASHIJIMA1) , Osamu MITARAI2) ,Atsushi FUKUYAMA3) and Yuichi TAKASE4)
IGSES, Kyushu University, 6-1 Kasuga-koen, Kasuga 816-8580, Japan
RIAM, Kyushu University, 6-1 Kasuga-koen, Kasuga 816-8580, Japan
2)
Tokai University, 9-1-1 Toroku, Higashi-ku, Kumamoto 862-8652, Japan
3)
RGPPE, Kyoto University, Nisikyo-ku, Kyoto 615-8540, Japan
4)
DCSE, University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa 277-8561, Japan
1)(Received 25 November 2014 / Accepted 21 April 2015)
Comparison between non-inductive plasma current start-up using electron cyclotron resonance heating(ECRH) with and without fundamental (1st) resonance using 8.2-GHz microwave is experimentally performedon QUEST. Results of soft X-ray measurements in diﬀerent energy ranges indicate significant diﬀerence in thenumber of current-carrying electrons with and without fundamental resonance. Numerical calculations show
eﬀective extendibility of electron energy in ECRH of fundamental resonance.
c 2015 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: spherical tokamak, plasma current start-up, electron cyclotron resonance heating, current-carrying
electron, soft X-ray
DOI: 10.1585/pfr.10.3402066

1. Introduction
Because of their higher compactness with low aspectratio (A = R/a: R the major radius and a the minor radius), spherical tokamaks (STs) are the leading candidates
for economically eﬃcient fusion reactors. STs are capableof stably confining high-β plasmas (β denoting the ratio ofplasma pressure to magnetic pressure) [1]. In conventional
tokamaks, Ohmic heating (OH) using a toroidal electricfield inductively-induced by the time variation of the current through the center solenoid (CS) coil is the main
method to generate and control plasma current. Because
space is limited in the high-field side of a ST, non-inductiveplasma current start-up is an indispensable technique. Experiments of non-inductive plasma current start-up using
electron cyclotron resonance heating (ECRH) have been
actively performed in ST such as LATE [2], MAST [3],TST-2 [4] and QUEST [5, 6]. In the experiments, thecombined eﬀect of fundamental (1st) and second harmonic(2nd) ECRH provides a significant plasma heating [2, 5],
and it is also reported the energetic electrons confined in
an open magnetic surface plays an essential role in plasma
current start-up [5, 6]. In conventional tokamaks, plasma
production with 2nd ECRH has been reported [7, 8] and aauthor’s e-mail: miura@triam.kyushu-u.ac.jp∗) This article is based on the presentation at the 24th International Toki
Conference (ITC24).

plausible explanation has been developed [9, 10]. Nevertheless, plasma current start-up without 1st ECRH has notbeen reported yet.
Our challenge is to make a directly-compared surveyof the eﬀectiveness of ECRH in plasma current start-up
with and without 1st ECRH.
The experimental setup is described in Section 2. Theresults of experiments are presented in Section 3. The numerical calculation on the eﬃciency in energy absorption
from the electric field to electrons is presented in Section
4. A summary is presented in Section 5.

2. Experimental Apparatuses
Experiments have been performed on QUEST, which
is a middle-sized ST with R = 0.64 m, a = 0.40 m, andtoroidal magnetic field BT < 0.25 T, and electron cyclotron
wave with frequency of 8.2 GHz, O-mode is launched on
the mid-plane of the vessel as the main heating source. Thevacuum magnetic field configuration in the experiments
has a positive n-index and there is no magnetic-field null
inside of the vacuum vessel (Fig. 1). The magnetic configuration plays an essential role in confining the energetic
electrons [5,6] and gives successful plasma current start-up
with 1st ECRH of 8.2 GHz [5, 6]. In the set of experiments
for the study, the same vertical field is adopted unless otherwise stated.

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c 2015 The Japan Society of Plasma
Science and Nuclear Fusion ResearchPlasma and Fusion Research: Regular Articles

Volume 10, 3402066 (2015)

Fig. 1 Typical contours of the poloidal flux (a) without and (b)with plasma current (#24498 2.2 s). Outlines of the vacuum vessel and the poloidal coils are also shown. The
vertical lines indicates the position of 1st (solid), 2nd(dashed) and 3rd (dashed-dotted) ECR layers. A solid
circle in Fig. 1 (a) indicates the viewing area of the 2DSXR camera which are 26 - 62 cm on toroidal directionand −18 - +18 cm on vertical direction.

Fig. 2 Top cross-sectional views of the vessel and visible areaof both the SBD and the 2D-SXR detectors. (a): Loci ofthe 1st (solid), the 2nd (dashed) and 3rd (dashed-dotted)
ECR layers of Fig. 1 (a) are drawn with R = 29 cm, 58 cm
and 87 cm, respectively. (b): Loci of the 2nd (dashed)and 3rd (dashed-dotted) ECR layers are given with R =31 cm and 48 cm, respectively.

Two types of soft X-ray (SXR) measurement are usedin the experiments. One is a surface barrier diode (SBD)
and another is a two-dimensional SXR (2D-SXR) camera.
The detectable energy range of the SBD is from 10 eV to80 eV. The SBD is located on the mid-plane to monitor
the whole plasma. The energy sensitivity of the 2D-SXR
camera was regulated in the range of 60 - 80 eV to detect
the production of current-carrying electrons. The viewing
area of the camera can be illustrated in Fig. 1 and Fig. 2.

3. Experimental Results
Typical waveforms for the start-up experiments withand without 1st ECRH are shown in Fig. 3. Plasma production and plasma current start-up take place almost simultaneously as observed in the signals of Hα, SXR and plasma
current. Plasma currents of 8 kA and 3 kA were achieved
with and without 1st ECRH, respectively. To improve theFig. 3 Typical waveforms of plasma current, RF power, Hα intensity and SXR intensity detected by the SBD in 1stECRH plasma current start-up (#24498) (left) and thosewith 2nd ECRH (#25673) (right). The location of theECR layers in each plasma is illustrated in Fig. 2.

Fig. 4 The toroidal field coil current dependence on the generated plasma current. Data below ITF = 17 kA (without1st ECRH) in the range of 68 - 70 kW and data above ITF= 21 kA (with 1st ECRH) in the range of 65 - 70 kW areplotted. ITF = 26.6 kA corresponds to the major radius of
1st ECR (R1st ECR ) = 29 cm, R2nd ECR = 58 cm and R3rd ECR= 87 cm. For ITF = 18 - 21 kA, as the 1st ECR is locatedat RECR = 20 - 23 cm, where the gap is between the innervessel and the inner protector, and the operation is prohibited. The three symbols represent data at ECR from different vertical field strengths of 2.6 mT (circles), 2.7 mT(triangles), and 3.2 mT (squares).

reproducibility of the plasma production, the RF power forthe 2.45 GHz is applied just before the injection of the RFpower for 8.2 GHz. Indeed, it should be noted (Fig. 3) thatthe application of 2.45 GHz cannot produce plasma current
except pressure driven current. (∼0.5 kA). To drive further
plasma current, it is necessary to produce energetic electrons which have the capability to drive plasma current due
to the intrinsic toroidal asymmetric confinement in co andcounter drift direction [4–6]. As plasma current starts up
just after the termination of the injection of 2.45 GHz, thepre-injection of the 2.45 GHz RF does not play an essential
role in the plasma current start-up. The generated plasma
current without 1st ECRH is significantly lower than thatwith 1st ECRH even in the nearly identical poloidal magnetic configuration. From the ECR location dependence(Fig. 4), higher toroidal fields can provide higher plasma

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Fig. 5 Plasma current vs RF power without 1st ECRH. The 2ndECR is located in the range of R2nd ECR = 30 - 37 cm, and
ITF = 14 - 17 kA.

Fig. 7 The ratio between the SXR detected by the SBD and Hαis plotted as a function of plasma current. Circles andsquares show data with 1st ECRH (#24495-24502) andwithout 1st ECRH (#25673-25677), respectively.

representing 2nd ECRH is significantly less than that in 1stECRH.

4. Numerical Calculation of Electron
Energy Absorbed from ElectricField
Fig. 6 (a) The relationship between SXR intensity as measuredby the 2D-SXR camera and plasma current is the samethat obtained with the SBD. Circles and squares show
the data with 1st ECRH (#25688) and without 1st ECRH(#25669-25677), respectively. (b) Enlarged view of data
without 1st ECRH.

currents in all cases. Plasma current with 1st ECRH is
usually higher than that without 1st ECRH. The generated plasma current also depends on the injected RF power(Fig. 5). Breakdown and production of pressure driven current occur during injection with RF power below 65 kW,
but without initiating any other plasma current. Plasmacurrent flows without 1st ECRH when the RF power isabove 65 kW. Higher plasma current is generated by increasing the RF power. The total intensity of SXRs detected with the 2D-SXR camera is plotted as a function ofthe plasma current (Fig. 6). Values have an apparent positive correlation with plasma current and this indicates thatenergetic electrons drive plasma current. It has already reported that current-carrying electrons on QUEST has theenergy in the range of 100 eV to several keV during theplasma current start-up phase [11]. This correlation can beobtained in the previous observations on vertical-field dependence at plasma current start-up with 1st ECRH [12].
The relation between the ratio of SBD to Hα intensities andplasma current is presented in Fig. 7. This ratio is favoredas a monitor of the number of energetic electrons. A significant diﬀerence in the ratio between with and without 1stECRH is obtained. Only the toroidal field strength is adjusted to switch harmonics patterns in the vacuum vessel.
This strongly indicates that the diﬀerence in heating mechanism gives rise to the diﬀerence in the number of energetic
electrons and plasma current. One should be considered
how the number of energetic electron in higher harmonics

The electron energy is sourced from the electrical fieldof the high-frequency wave when electrons pass throughthe ECR layer is calculated using a model given in [9, 10].
The phase diﬀerence between the particle gyromotion andthe wave electric field as Ψ = nψ − ωt and the dimensionless variable Γ = γ − 1 are defined, where, n, ψ, ω, γ
are the harmonic number, the gyro-phase of electrons, thewave angular frequency, and relativistic factor of electron,respectively. Γmc2 is the kinetic energy of electrons and Γ
is the normalized kinetic energy of electrons and intrinsically Γ  1. The basic equations of Γ and Ψ are derived
from the Lorentz equation for electrons including relativistic eﬀect in the electric field of the microwave beam under
the assumption of kρL  1, where k, and ρL are the wave
number, Larmor radius of electron, respectively.
11dΨ= −Γω + √ εωΓ − 2 sin Ψdt
2 2= −Γω + εω cos Ψ(For n = 1)
(For n = 2),(1)dΓεω 1= − √ Γ 2 cos Ψdt2

(For n = 1)

= εωΓ sin Ψ(For n = 2).

(2)

Here ε ≡ eE/mcω is the ratio of the momentum changeof particles to mc during one wave period. The wave frequency is set at 8.2 GHz, injection RF power is 60 kW, andthe half-width of electrical field is set to 20 cm at 1st and2nd ECR. The time evolutions for the energy transfer toelectrons in 2nd ECR is presented in Fig. 8 (a). The initial
kinetic energy of the injected electron is Γ = 1 × 10−6 ,which corresponds to approximately room temperature.
This calculation indicates resonance electrons in the strong
electric field can be accelerated immediately, but the mostof the transferred energy is released when the electron
moves out of the strong electric field. Nevertheless, some

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Fig. 8 (a) Variation of Γ with initial energy, which is set to 1 ×10−6 for ωt of 2nd ECR. Γ oscillates when electrons passthrough the RF electrical field. The dashed line gives its
strength. (b) Variation of Γ with initial energy, which is
1 × 10−6 for Ψ of 2nd ECR.

culation finds that 3rd ECR is inherently more ineﬃcient.
Let Wout denote the electron energy at zero electric field
when an electron is passing through the electric-field atECR. From Wout for 1st and 2nd ECR given in Figs. 9 and
10 respectively, their maximum energies are 1.8 keV and
87 eV. Clearly, the maximum energy at 2nd ECR is much
lower than that at 1st ECR. 1st ECRH are possible to bemade current-carrying electrons, but 2nd ECRH is diﬃcult.
It is thought that the eﬀects of synergistic and stochastic
heating are necessary to produce current-carrying electrons
without 1st ECRH. In fact, stochastic heating is working
well to accelerate electron up to 8 keV at 1st ECRH [13] inthe same RF power, although the eﬃciency is not so high.

5. SummaryFig. 9 Absorbed energy at zero electric field as a function ofelapsed time through the high-frequency electric field at
1st ECR.

Plasma current start-up is achieved without 1st ECRH
using 8.2-GHz microwave. Plasma current tends to behigher with increasing RF power and toroidal field, although plasma current without 1st ECRH is always lessthan that with 1st ECRH. The number of current-carryingelectrons with 1st ECRH is higher than that without 1stECRH because of the total intensity of SXRs detected withthe 2D-SXR camera. The acceleration of electrons in 2nd
ECR is slower and electrons in 2nd ECR receives less energy from the RF electrical field from the numerical calculations. It is diﬃcult to generate current-carrying electronsin 2nd ECR. It is understood that 2nd ECR is inherently
ineﬃcient to start up plasma current. We confirm that ourresults from calculations were qualitatively consistent withexperimental results.

Acknowledgments
Fig. 10 Absorbed energy at zero electric field as a function ofelapsed time through the high-frequency electric field at
2nd ECR.

of the transferred energy is retained. The mechanism
is easy to understand by referring to the Γ - Ψ mapping(Fig. 8 (b)), where Ψ is the phase diﬀerence associated withthe electron cyclotron motion and the electrical field frequency multiplied by the harmonic number. In strong electric fields, electrons trace out ellipses, the size of which canbe determined by the strength of electric field on the Γ - Ψmap. Γ is an invariant of motion when the variation of electric field is significantly slower than the rotation frequency
for the ellipse. Breaking of the Γ invariance is the only
way to transfer energy to the electron and is required invarying the electron-aﬀected electric field strength as fast
as possible. The value of Γ for the ellipse at the sameelectric field in 2nd ECR is significantly lower than thatin 1st ECR. Moreover the rotation frequency strongly depends on the harmonic number and the frequency at 2ndECR is clearly lower than that in the 1st ECR. The cal-This work was partially supported by JSPS
KAKENHI (24226020, 24656559) and was performed
with the support and under the auspices of the NIFS
Collaboration Research program (NIFS13KUTR085,NIFS13KUTR093). This work was supported in part by
the Collaborative Research Program of Research Institutefor Applied Mechanics, Kyushu University.
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